Inestabilidades térmicas: célula de Bénard

En este trabajo se estudia el comportamiento de una lámina de fluido limitada por dos superficies. La temperatura de la superficie inferior es mayor que la de la placa superior. Para pequeños gradientes de temperatura la conducción de calor será suficiente para disipar el calor. Sin embargo, la convección de Bénard, es decir, el movimiento macroscópico de las partículas del fluido, comienza cuando la conducción no es capaz por sí sola de disipar todo el calor debido a un mayor gradiente de temperatura. La consecuencia más notable de la convección es la formación de las llamadas celdas de Bénard. Como se va a demostrar estas solo pueden adoptar determinadas formas geométricas. De hecho, solo pueden ser polígonos regulares y solo serán visibles cuando la diferencia térmica entre las superficies no sea excesivamente grande y el flujo no sea turbulento. Una característica importante de este tipo de sistemas es que las ecuaciones que las rigen no son lineales, y, por tanto, aparece el fenómeno del caos determinista.

高频振动影响下双层Marangoni-Bénard对流稳定性研究

对高频振动影响下双层Marangoni-Bénard对流进行了线性稳定性理论分析,发现了高频振动对于Marangoni-Bénard对流不稳定性特征的双重影响,并分析了硅油与氟液(FC70)典型双层流体实验系统的不稳定性,其结果显示在一定振动运动或残余重力场下的两层流系统具有更复杂的不稳定现象.

Oscillatory instability of Rayleigh-Marangoni-Bénard convection in two-layer liquid systems

The oscillatory behaviour of the Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) regarding two combinations of two-layer fluid systems has been investigated theoretically and numerically. For the two-layer system of Silicone oil (10cSt) over Fluorinert (FC70), both linear instability analysis and 2D numerical simulation show that the instability of the system depends strongly on the depth ratio Hr = H1/H2 of the two-layer liquid. The oscillatory regime at the onset of R-M-B convection enlarges with reducing Γ = Ra/Ma values. In the two-layer system of Silicone oil (2cSt) over water, it loses its stability and onsets to steady convection at first, then the steady convection bifurcates to oscillatory convection with increasing Rayleigh number Ra. This behaviour was found through numerical simulation above the onset of steady convection in the case of r = 2.9, ε=(Ra-Ruc)/Rac = 1.0, and Hr = 0.5. Our findings are different from the previous study of the Rayleigh-Benard instability and show the strong effects of the thermocapillary force at the interface on the time-dependent oscillations at or after the onset of convection. We propose a secondary oscillatory instability mechanism to explain the experimental observation of Degen et al. [Phys. Rev. E, 57 (1998), 6647-6659].

两相流层的Marangoni-Bénard不稳定性分析

关于液层的Marangoni-Bénard不稳定性的研究中,现有文献中普遍采用的是单层流模型.本文建立了一种新的两层流模型,采用线性稳定性方法对带有蒸发界面的两层流的Marangoni-Bénard对流不稳定性进行了分析,得到了在不同蒸发量下临界Marangoni数与波数的关系,重点讨论了蒸发速率对汽液两层流系统Marangoni-Bénard不稳定性的影响.

Rayleigh-Bénard热对流的动理论分析

利用基于分子动理论的直接模拟Monte Carlo(DSMC)方法,研究了 Rayleigh-Bènard问题.计算中,上下平板表面温度之比固定为0.1.Kn=0.01时,随着Ra数的增大,大约在1700附近,流动从热传导状态转变为热对流状态,DSMC计算得到的下平板热流与Ra数的关系与经典实验和理论结果相符.Kn=0.05时,流动保持稳定的热传导状态,Ra数的增大并不能引发热对流现象.

Experimental Study on Bénard-Marangoni Convection in Double Immiscible Liquid Layer

An experimental investigation of Bénard-Marangoni convection has been performed in double immiscible liquid layers of rectangular configuration on the ground. The two kinds of liquid are 10cst silicon oil and FC-70 respectively. The size of rectangular chamber is 100mm×40mm in horizontal cross-section. The evolution processes of convection are observed in the differential thickness ratio of two liquid layers. The critical temperature difference was measured via the detections of fluid convection by a particle image velocimetry (PIV) in the vertical cross-section of the liquid layer. The critical temperature difference or the critical Marangoni number was given. And the influence of the thickness ratio of two liquid layers on the convection instability was discussed. The evolution processes of patterns and temperature distributions on the interface are displayed by using thermal liquid crystal. The velocity distributions on the interface were also obtained. In comparison with the thermocapillary effect, the effect of buoyancy convection will relatively increase when the depth of the liquid layer increases. Because of the coupling of buoyancy and thermocapillary effect, the convection instability is much more complex than that in the microgravity environment. And the critical convection depends on the change of the thickness of liquid layers and also the change of thickness ratio of two liquid layers.

Rayleigh-Marangoni-Bénard Convective Instability

The Rayleigh-Marangoni-Benard convective instability (R-M-B instability) and flow patterns in the two-layer system of silicon oil 10cSt and Fluorinert FC70 liquids are studied theoretically and experimentally. Both linear instability analysis and 2D numerical simulation (A=L/H=10) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. Time-dependent oscillations arising at the onset of convection were investigated in a larger various range of two-layer depth ratios (Hr=H1/H2) from 0.2 to 5.0 for different total depth less than 12mm. Our results are different from the previous study on the Rayleig-B閚ard instability and show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. Primary experimental results of the critical instability parameters and the convective structure in the R-M-B convection have been obtained by using the digital particle image velocimetry (DPIV) system, and a good agreement in comparison with the results of numerical simulation was obtained.

两层液体Bénard-Marangoni对流的实验研究

采用粒子图像测速技术(PIV)对两层流体B(en)ard-Marangoni对流进行了实验研究.研究了各种不同厚度比下的临界对流模式,同时研究了在温差变大时向超临界对流模式转化过程.实验结果表明,界面张力对各种对流模式的形成和转变具有重要的作用.

Dynamic states in rotating Rayleigh-Bénard convection systems

A new geometry-independent state - a traveling-wave wall state - is proposed as the mechanism whereby which the experimentally observed wall-localized states in rotating Rayleigh-Bénard convection systems preempt the bulk state at large rotation rates. Its properties are calculated for the illustrative case of free-slip top and bottom boundary conditions. At small rotation rates, this new wall state is found to disappear. A detailed study of the dynamics of the wall state and the bulk state in the transition region where this disappearance occurs is conducted using a Swift-Hohenberg model system. The Swift-Hohenberg model, with appropriate reflection-symmetry- breaking boundary conditions, is also shown to exhibit traveling-wave wall states, further demonstrating that traveling-wave wall states are a generic feature of nonequilibrium pattern-forming systems. A numerical code for the Swift-Hohenberg model in an annular geometry was written and used to investigate the dynamics of rotating Rayleigh-Bénard convection systems.